Translation of abstract (English)

The Jeans instability of a galactic disk embedded in a dynamically responsive dark-matter halo is investigated in this work. On small scales the instability is suppressed, if the Toomre stability index Q_T is higher than a certain threshold, but on large scales the Jeans instability sets invariably in. However, using a simple self-consistent disk-halo model it is demonstrated that this occurs on scales which are much larger than the system so that this is indeed only a nominal effect. Also, a rigorous calculation of the dynamical friction (DF) force exerted on a Plummer and a Hernquist sphere moving through an infinite homogenous system of field stars is presented. By using a wave-mechanical treatment, we recover Chandrasekhar's drag force law with a modified Coulomb logarithm that depends on the exact shape of the perturber. We then extend this mode analysis to anisotropic velocity distributions of the field stars. We present easy-to-use handy formulae of the DF force exterted on a point-mass satellite for the cases when the velocity ellipsoid is either oblate or prolate for different values of the effective velocity dispersion sigma_eff determining the anisotropy of the host system.